{"paper":{"title":"Extended Frege proofs, circuits and rewriting","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.LO","authors_text":"Jan Krajicek","submitted_at":"2026-06-11T13:53:03Z","abstract_excerpt":"Inspired by a statement about Extended Frege proof systems by Jain and Jin (FOCS 2022) we prove that:\n  - there is a p-time binary relation $\\approx$ between circuits that implies their logical equivalence,\n  - the relation $\\approx$ implies that each of the two circuits can be rewritten into the other one by possibly deleting some gates and adding at most seven new gates,\n  - if the equivalence $C \\equiv D$ has a size $s$ proof in an Extended Frege or a Circuit Frege proof system then there is a chain of circuits $E_i$ $$ C = E_0 \\approx \\dots \\approx E_t = D $$ with $t \\le s^{O(1)}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13367","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.13367/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}